Here is Jobs' letter to his fellow Apple employees (and the legions of faithful customers) in full:

I
have always said if there ever came a day when I could no longer meet my duties
and expectations as Apple's CEO, I would be the first to let you know.
Unfortunately, that day has come.

I hereby resign as CEO of Apple. I would like to serve, if the Board sees fit,
as Chairman of the Board, director and Apple employee.

As far as my successor goes, I strongly recommend that we execute our
succession plan and name Tim Cook as CEO of Apple.

I believe Apple's brightest and most innovative days are ahead of it. And I
look forward to watching and contributing to its success in a new role.

I have made some of the best friends of my life at Apple, and I thank you all
for the many years of being able to work alongside you.

Steve

Here is the press release in full regarding the handoff in power to Tim Cook:

Tim Cook Named CEO and Jobs Elected Chairman of the Board

CUPERTINO, Calif.--(BUSINESS WIRE)--Apple's Board of Directors today announced that Steve Jobs has resigned as Chief Executive Officer, and the Board has named Tim Cook, previously Apple's Chief Operating Officer, as the company's new CEO. Jobs has been elected Chairman of the Board and Cook will join the Board, effective immediately.

"Steve has made countless contributions to Apple's success, and he has attracted and inspired Apple's immensely creative employees and world class executive team. In his new role as Chairman of the Board, Steve will continue to serve Apple with his unique insights, creativity and inspiration."

"Steve's extraordinary vision and leadership saved Apple and guided it to its position as the world's most innovative and valuable technology company," said Art Levinson, Chairman of Genentech, on behalf of Apple's Board. "Steve has made countless contributions to Apple's success, and he has attracted and inspired Apple's immensely creative employees and world class executive team. In his new role as Chairman of the Board, Steve will continue to serve Apple with his unique insights, creativity and inspiration."

"The Board has complete confidence that Tim is the right person to be our next CEO," added Levinson. "Tim's 13 years of service to Apple have been marked by outstanding performance, and he has demonstrated remarkable talent and sound judgment in everything he does."

Jobs submitted his resignation to the Board today and strongly recommended that the Board implement its succession plan and name Tim Cook as CEO.

As COO, Cook was previously responsible for all of the company's worldwide sales and operations, including end-to-end management of Apple's supply chain, sales activities, and service and support in all markets and countries. He also headed Apple's Macintosh division and played a key role in the continued development of strategic reseller and supplier relationships, ensuring flexibility in response to an increasingly demanding marketplace.

Apple designs Macs, the best personal computers in the world, along with OS X, iLife, iWork and professional software. Apple leads the digital music revolution with its iPods and iTunes online store. Apple has reinvented the mobile phone with its revolutionary iPhone and App Store, and has recently introduced iPad 2 which is defining the future of mobile media and computing devices.

Steve Jobs and his friend Steve Wozniak founded Apple Computer in 1976. He left the company in 1985 following a bitter power struggle with then CEO John Sculley (former CEO of Pepsi-Cola) and went on to found NeXT Computer. Jobs would later return to Apple in the capacity of "Interim Chief Executive" in the fall of 1997, and later officially regained the title of CEO.

Since that time, Jobs has overseen a massive resurgence for Apple with the launch of Apple Retail Stores, the original iMac, iPod, the iPhone, and the iPad -- each of which has made huge waves in their respective markets (not to mention other successes in between like the iTunes Music/App Store, OS X, etc.). Just this week, it was revealed that Apple's retail stores rake in $5,226 per square foot, more than any other retailer in the United States.